Energetic proton transport through self-generated Alfvén waves in
impulsive (γ-ray) flares is studied using the method of Monte Carlo
simulations. Protons are traced inside a flux tube after they are released from
a point source located inside the loop until they hit the boundary of the 1-D
simulation box and escape. As they stream from the source towards the
boundaries, the particles generate Alfvén waves through the streaming
instability. We consider both open and closed field lines. In the closed field
line case, the escaping particles precipitate and produce observable secondary
emissions; for the open field line, particles precipitate only from one end of
the field line, and escape freely to the interplanetary medium from the other
end. For a sufficiently large number of accelerated protons per unit area, where n0 is the plasma density,
the Alfvén speed, and the proton
gyro-frequency, the particle flux from the source produces a turbulent trap that
expands at Alfvén speed in both directions from the source. The resulting
γ-ray emission from the loop legs consists of a precursor, related to
the quick propagation of particles when the trap has not formed yet, and of a
delayed brightening in the loop leg closer to the source, related to the opening
of the turbulent trap as the self-generated waves reach the solar surface. For
impulsive injections lasting , where L is the loop
length, the second emission may be suppressed by adiabatic deceleration in the
expanding turbulent trap. For open field lines, our model is capable of
producing the small ratio of the numbers of interplanetary-to-interacting
protons typically observed in impulsive flares, if the proton source is located
close to the Sun.

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